MCL version 3 (regular alternation-free mu-calculus) [MS03, Mat06]
is an extension of the alternation-free fragment of the modal mu-calculus
[Koz83, EL86] with action predicates similar to those of ACTL [DV90] and
regular expressions over action sequences similar to those of PDL [FL79].
In the temporal formulas of MCL version 3, the LTS actions are merely character
strings.

MCL version 3 is supported by the evaluator3
on-the-fly
model checker.

MCL version 4 (value-passing modal mu-calculus) [MT08] is an
extension of MCL version 3 with data-handling constructs (data variables,
expressions, parameterized fixed point operators, programming language
constructs) and an infinite looping operator similar to that of PDL-delta
[Str82], able to express fairness properties. In the temporal formulas of
MCL version 4, the LTS actions are tuples containing channel names and
data values, which can be extracted and used in calculations, as originally
proposed in the RICO logic [Gar89].